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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Low-pass(LP) Filter A low-pass(LP) filter is a filter that passes low- frequency signals but attenuates (reduces the amplitude of) signals with frequencies higher than the cutoff frequency. A low-pass(LP) filter is the opposite of a high-pass(HP) filter.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Continuous-time LP Filter An ideal LP filter completely eliminates all frequencies above the cutoff frequency while passing those below unchanged. Ideal LP frequency response is a rectangular function, and is a brick-wall filter. The transition region present in practical filters does not exist in an ideal filter.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Frequency response of 1 st order LP Filter The gain-magnitude frequency response of a first-order (one-pole) low-pass filter. The voltage gain is shown in decibels.At cut-off frequency there is a 3 dB decline.Angular frequency is shown in units of radians per second.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Stop-band response of LP Filter For a first-order LP filter,the attenuation rate in the stop-band is 20 dB per decade. A second-order filter attenuates higher frequencies more steeply. In general a second-order Butterworth filter exhibits the 40 dB per decade attenuation rate in the stop-band. Other all-pole second-order filters may roll off at different rates initially depending on their Q-factor, but approach the same final rate of 40 dB per decade. Third- and higher-order filters are defined similarly. In general, the final rate of power roll off for a n th order LP filter is 20n dB per decade.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Passive RC first order LP filter : The combination of resistance and capacitance gives you the time constant of the filter τ = RC (represented by the Greek letter tau)

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA An active low-pass filter This 1st-Order low pass Butterworth type filter, consists simply of a passive RC filter connected to the input of a non-inverting operational amplifier. The frequency response of the circuit will be the same as that of the passive RC filter, except that the amplitude of the output signal is increased by the pass band voltage gain of the amplifier. The gain in the pass band is −R 2 /R 1 First-order Low Pass Butterworth Filter First-order Low-Pass(LP) Butterworth Filter

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Frequency response of 1 st order HP Filter The cutoff frequency for a high-pass filter is that frequency at which the output voltage equals 70.7% of the input voltage. Above the cutoff frequency, the output voltage is greater than 70.7% of the input, and vice versa.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Band-pass(BP) filter The Band-Pass(BP) filter passes a selected range or band of frequencies that can be either narrow or wide while attenuating all those outside of this range. The Band-Pass(BP) filter can be of two types: Broad-band Band-Pass filter Narrow-band Band-Pass filter

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Wide-band and narrow-band BP Filter The "Q" of a BP filter is the ratio of the Resonant Frequency, (ƒ r ) to the Bandwidth(BW) and is given as: : : In BP Filter, the width of the pass-band between the upper and lower-3dB corner points determine the Quality Factor(Q-point) of the circuit. This Q Factor is a measure of how "Selective" or "Un-selective" the band pass filter is towards a given spread of frequencies. The lower the value of the Q factor the wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more "selective" is the filter.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Band-Reject(BR) Filter A band-stop filter or band-rejection filter passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a very narrow stop band.(high Q factor).Notch filters are used in live sound reproduction(Public Address systems, also known as PA systems) and in instrument amplifier(especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin etc.) to reduce the noise and unwanted frequencies.Public Address systemsinstrument amplifier e.g., Anti-hum filter is used to filter out the mains hum from a 50 Hz power line, though its higher harmonics could still be present. The filter passes all frequencies, except for the range of 49–51 Hz.mains humpower line

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA All-pass Filter The all-pass filter is an important building block in audio signal processing systems. It is called all-pass because all frequencies are passed equally. signal In other words, the amplitude response of an all-pass filter is any nonzero constant at each frequency, but filter changes the phase relationship between various frequencies.amplitude responsephase Generally, the first-order all-pass filter is described by the frequency at which the phase shift crosses 90°phase shift

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA Phase response of 1 st order All-pass Filter For 1 st order all-pass filter,the amplitude response is flat (within the bandwidth limitation of the amplifier), and there is a 90 degree phase shift at the "corner" frequency.

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Department of Electronics and Communication Engineering, Manipal Institute of Technology, Manipal, INDIA All pass filters are most often used for following: for matching phase in systems where phase is important for producing delays in circuits that need to delay a signal for creating 90 o shifts for quadrature modulators Applications of All-pass Filters